Cook oil and shallots 5 minutes over moderate heat. Whisk in the peanut butter, coconut milk, lemon juice and soy sauce. Stir in water and cook, stirring often, for 5 minutes. Stir in brown sugar and chili paste. Cook 5 minutes more. Mixture will have cooked down and thickened somewhat. Remove from heat and stir in basil. Serve warm. Makes about 2 1/2 cups of sauce.